The research combines computer simulation (energy optimization and normal mode analysis at the level of neighboring base pairs) with new developments in the theory of elastic rods to examine the configurations and properties of supercoiled DNA, a topologically constrained form of the double helix subject to higher-order folding and compensatory strand twisting. Sequence-dependent features of the long, threadlike polymer are incorporated in the theory of elastic rods and treated by numerical simulations. By combining analytical studies with computer simulations, we obtain complementary information and have a series of built-in checks and balances for assessing the significance of our findings. The computational results stimulate new theoretical developments, which in turn can be used to assess the validity of the calculations. The effects of the polyelectrolyte backbone and local chemical environment are treated implicitly with knowledge-based potentials extracted from high resolution structures of double helical DNA and, in representative cases, with explicit treatment of electrostatic forces. Our immediate goal is to describe chain configuration and properties in terms of realistic molecular models. The proposed studies may clarify the role of primary chemical features (base sequence, sugar-phosphate backbone) and ligand binding (proteins, drugs) on the overall folding of the double helix. We aim to develop an accurate and comprehensive model of the configurational properties of the DNA loops tethered to the Lac repressor-operator assembly with the possibility of learning new details about the role of DNA structure in the regulation of transcription. A second goal is to uncover structural details of supercoil-induced transitions of DNA, such as the helical unwinding implicated in biological processes. Among the scientific issues to be addressed are: (1) the role of sequence-dependent local structure and specific protein conformation on the global features of supercoiled chains; (2) the role of sequence and ligand binding on large-scale configurational transitions of spatially constrained DNA; (3) the competing effects of multiple proteins on the shape and deformability of the supercoiled duplex; (4) the interplay of local and global structure in supercoiling dynamics; (5) the effect of ionic conditions on loop configuration.